A0389
Title: The modified conditional sum-of-squares estimator for fractionally integrated models
Authors: Mustafa Kilinc - WHU - Otto Beisheim School of Management (Germany) [presenting]
Michael Massmann - WHU - Otto Beisheim School of Management (Germany)
Abstract: The aim is to analyze the influence of estimating a constant term on the bias of the conditional sum-of-squares (CSS) estimator of the fractional parameter, say $d$, and other parameter estimates of the short-run dynamics in a stationary or non-stationary time series model. We first consider a ``type II'' ARFIMA(0,$d$,0) model including a constant term and derive an expression for the leading bias term of $\hat{d}$. We show that we can easily remove the bias in $\hat{d}$ that occurs due to the presence of a constant term by a simple modification of the CSS objective function. Consequently, the estimated fractional parameter, say $\hat{d}_m$, behaves on average the same as if we had known the true value of the constant term, discounting the higher-order bias terms. We call this new estimator the modified conditional sum-of-squares estimator (MCSS). The remaining part of the leading bias of $\hat{d}_m$ is pivotal and can be completely eliminated by a simple bias correction. We later generalize our analysis to the case where the short-run dynamics take a more general structure than the simple $i.i.d.$ shocks. The importance of bias correction is highlighted through empirical illustrations in macroeconomics and hydrology time series.
